How to factor 4x^3 -4x+16 ?
how can i factor it when its missing the ^2 term ?
To factor the polynomial 4x^3 - 4x + 16, even though it's missing the x^2 term, you can still follow a specific method called the "factor by grouping" or "grouping method."
Here's how to factor it step-by-step using the grouping method:
Step 1: Group the terms
Take the first two terms, 4x^3 - 4x, and group them together. Write them as a common factor:
4x(x^2 - 1)
Step 2: Factor the common factor
Now, factor out the common factor, which is 4x:
4x(x^2 - 1)
Step 3: Group the remaining terms
Group the remaining term, +16, separately:
4x(x^2 - 1) + 16
Step 4: Factor the common factor (Differences of squares)
In the parentheses, x^2 - 1, we recognize that it is a difference of squares because we can rewrite it as (x)^2 - (1)^2. A difference of squares can be factored as (a + b)(a - b):
4x(x + 1)(x - 1) + 16
Now, you have factored the polynomial 4x^3 - 4x + 16 as 4x(x + 1)(x - 1) + 16.
Thus, the factored form of the polynomial is 4x(x + 1)(x - 1) + 16.